Answer to Question #149613 in Classical Mechanics for Noah Bartos

Question

Two arrows are shot from opposite sides of a 4.0m deep canyon. The arrows land in the same spot on the floor of the canyon at the same time. One is shot at an 80 degree angle, the other is shot at a 20 degree angle. The total time it takes the arrow shot at 80 degrees to land is 14 seconds. How do you determine the initial velocity of either of the arrows

Answer 1

$$y=h-v_1\sin{80}t+0.5gt^2\\=h+v_2\sin{20}t-0.5gt^2=0\\4+v_2\sin{20}(14)-0.5(9.8)(14)^2=0\\ v_2=200\frac{m}{s}$$

$$4+v_1\sin{80}(14)-0.5(9.8)(14)^2=0\\ v_1=69\frac{m}{s}$$